What is factor x^6y^9-1 ?

The solution to factor x^6y^9-1 is (x^2y^3-1)(x^4y^6+x^2y^3+1)

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factor x^6y^9-1

factor

x^{6} y^{9} - 1

(x^{2} y^{3} - 1) (x^{4} y^{6} + x^{2} y^{3} + 1)

Solution steps

x^{6} y^{9} - 1

Apply exponent rules

= (x^{2} y^{3})^{3} - 1^{3}

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(x^{2} y^{3})^{3} - 1^{3} = (x^{2} y^{3} - 1) ((x^{2} y^{3})^{2} + x^{2} y^{3} + 1^{2})

= (x^{2} y^{3} - 1) ((x^{2} y^{3})^{2} + x^{2} y^{3} + 1^{2})

Simplify

(x^{2} y^{3})^{2} + x^{2} y^{3} + 1^{2} : x^{4} y^{6} + x^{2} y^{3} + 1

= (x^{2} y^{3} - 1) (x^{4} y^{6} + x^{2} y^{3} + 1)

x^{4} + 3 x^{3} - 27 x - 81

\frac{( f ( 5 + h ) - f ( 5 ) )}{h}

(4 x^{2} - 12 x + 9) \cdot m^{2}

3 x^{2} - 7 x y + 2 y^{2}

64 x^{6} \cdot y^{3} - 8 x^{3} \cdot y^{6}

What is factor x^6y^9-1 ?
The solution to factor x^6y^9-1 is (x^2y^3-1)(x^4y^6+x^2y^3+1)